1. Technical Field
The invention is related to image denoising, and in particular, to a technique for estimating denoised color images as a probabilistic function of estimated regions and estimated blurs at edges between the estimated regions of noisy images.
2. Related Art
Image denoising is a common problem in image processing. Early approaches to image denoising often focused on optimal filtering (such as Wiener filtering) for Gaussian image and noise processes and heuristic algorithms such as median filtering. Many modern denoising schemes use statistical models that are defined either directly on pixel neighborhoods or on filtered versions of the noisy image. In either case, conventional denoising schemes generally attempt to preserve meaningful edges in the image while suppressing unwanted noise in the image.
Unfortunately, conventional denoising schemes typically fail to adequately capture the piecewise smooth nature of objects as perceived by human viewers. It is well known that the perception of image noise is subject to masking, i.e., noise is more perceptible in smoothly shaded regions than in highly textured (high variance) regions. Anecdotally, people find color noise resulting from large gains in digital cameras set to high-ISO ratings quite objectionable, since this adds artificial high-frequency coloration to what people know should be uniformly colored objects. Furthermore, the artificial increase in sharpness that tends to occur with techniques such as anisotropic diffusion and bilateral filtering can destroy the natural softness at intensity edges and lead to a “cartoonish” (or banded) appearance in denoised images.
For example, a number of conventional denoising schemes use wavelets in an attempt to denoise images. However, when a natural image is decomposed into multiscale oriented subbands, highly kurtotic marginal distributions are often observed (as opposed to the marginal distribution of a Gaussian process, which typically has low kurtosis). To enforce the marginal distribution to have high kurtosis, wavelet based techniques typically suppress low-amplitude wavelet coefficient values while retaining high-amplitude values, a technique frequently referred to as “coring.”
One such coring technique operates by finding the joint distribution of wavelets to be correlated. Joint wavelet coefficients are simultaneously inferred in a small neighborhood across a range of subbands of different orientations and scales. The typical joint distribution for denoising is a Gaussian scale model (GSM) for generating a denoised copy of the input image.
Unfortunately, wavelet-based denoising schemes often introduce certain “ringing artifacts” into the denoised image. In other words, such schemes tend to introduce additional edges or structures in the denoised image.
Another type of conventional denoising scheme involves the use of simple Gaussian filtering to generate a denoised image. Such Gaussian filtering is generally equivalent to solving an isotropic heat diffusion equation represented by a second order linear partial differential equation (PDE). Unfortunately, edges in such denoised images tend to become blurred. Related conventional denoising schemes use “anisotropic diffusion” to keep edges sharp in the denoised image. Unfortunately, denoising schemes based on anisotropic diffusion tend to over-blur the image or artificially sharpen region boundaries (edges).
Related denoising schemes operate by learning a complete prior model over the entire image from marginal distributions. Such schemes sometimes use Bayesian inference for denoising or restoration of the input image. The resulting PDE is qualitatively similar to anisotropic diffusion but is based on learned prior models. Unfortunately, learning such priors (i.e., Gibbs distributions), using conventional techniques such as Markov chain Monte Carlo (MCMC) techniques tend to be computationally inefficient. Furthermore, these methods share some of the drawbacks of anisotropic diffusion, i.e., occasional over-blurring (over-smoothing) and edge/region boundary sharpening.
An alternative adaptation of Gaussian filtering uses a technique referred to as bilateral filtering to preserve edges by accounting for both space and range distances. Bilateral filtering techniques have been widely adopted for denoising images, particularly for color images in recovering high dynamic-range (HDR) images. Unfortunately, such schemes are unable to effectively deal with speckle noise in images. Further, as with Gaussian filtering and anisotropic filtering, bilateral filtering based denoising schemes also sometimes over-smooth and over-sharpen edges in the denoised image.
Other denoising techniques take advantage of cases where there are multiple images of a static scene to provide image denoising. Such schemes generally operate by estimating pixel means from multiple input images to remove the noise in an output image where both the scene and camera are static. Unfortunately, such “non-local” denoising schemes are not generally practical for use in denoising a single image. However, in the case where individual images have a sufficient number of repeating patterns, related techniques operate to approximate temporal pixel means as a function of spatial pixel means. In particular, as long as there are enough similar patterns in a single image, patterns similar to a “query patch” can be identified and used to determine the mean or other statistics to estimate true pixel values for denoising the image. These non-local methods work well for texture-like images containing many repeated patterns, but fail with images where there are not many repeating patterns. Furthermore, such methods tend to be computationally expensive as compared to other conventional denoising schemes.